Does there have to be one, surely its one and the same thing.
I guess a sanctuary, as Hugo's there has said, has a select criteria of animals they take in, they are probably more organised about quarantine, numbers and finances. However anybody who sets up a rescue must be a bit of a softie and a glutton for punishment!
I just mean at what point do you call yourself a sanctuary? Is it someone who appeals for help with funding and is open to take in rabbits on recommendation rather than seeking out rabbits themselves?